Abstract
We prove the Iwasawa Main Conjecture over the arithmetic \({\mathbb {Z}}_p\)-extension for semistable abelian varieties over function fields of characteristic \(p>0\).
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Notes
If \(g=1\) and \(\Delta \) denote the global discriminant, then \(\delta =\frac{\deg (\Delta )}{12}\) (see e.g. [20, eq. (9)]).
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Acknowledgments
The fourth author has been supported by EPSRC and JSPS. He would like also to express his gratitude to Takeshi Saito for his hospitality at the University of Tokyo where part of this work has been written. Authors 2, 3 and 4 thank Centre de Recerca Matemàtica for hospitality while working on part of this paper. Authors 1, 2 and 3 have been partially supported by the National Science Council of Taiwan, grants NSC98-2115-M-110-008-MY2, NSC100-2811-M-002-079 and NSC99-2115-M-002-002-MY3 respectively. It is our pleasure to thank NCTS/TPE for supporting a number of meetings of the authors in National Taiwan University. Finally, we are grateful to the anonymous referee for her or his careful reading.
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Lai, K.F., Longhi, I., Tan, KS. et al. The Iwasawa Main Conjecture for semistable abelian varieties over function fields. Math. Z. 282, 485–510 (2016). https://doi.org/10.1007/s00209-015-1550-4
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DOI: https://doi.org/10.1007/s00209-015-1550-4